# A line ax + y = 8 is perpendicular to 3x + 8y = 16. If the line ax + y = 8 passes through (8, 2) what is the value of a?

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The line ax + y = 8 is perpendicular to 3x + 8y = 6.

The product of the slope of two perpendicular lines is -1. Writing 3x + 8y = 6 in the slope intercept form gives `y = -(3/8)x + 6/8` . The slope of the line is `-3/8` . As ax + y = 8 is perpendicular, the slope of the line is `8/3` .

ax + y = 8

=> y = -ax + 8

=> `-a = 8/3`

=> a = `-8/3`

**The value of a = `-8/3` **